<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="2020" minor="2"/>
<Label-Scheme value="2" prefix=""/>
<View-Properties presentation="true" autoexpanding_sections="true" UserProfileName="Maple Default Profile" NumericFormat-ApplyInteger="true" NumericFormat-ApplyRational="true" NumericFormat-ApplyExponent="false" editable="true">
</View-Properties>
<MapleNet-Properties prettyprint="3" warnlevel="3" compactdisplay="false" preplot="" helpbrowser="standard" displayprecision="-1" echo="1" unitattributes="&quot;fontweight&quot; = &quot;bold&quot;" imaginaryunit="I" longdelim="true" elisiontermsthreshold="10000" elisiondigitsafter="100" elisiondigitsbefore="100" plotdevice="inline" errorbreak="1" plotoptions="" plotdriver="opengl" quiet="false" elisiontermsbefore="100" elisiontermsafter="100" historytimestamp="false" screenwidth="79" indentamount="4" plotoutput="terminal" screenpixelheight="1080" rtablesize="[10, 10]" useclientjvm="true" labelwidth="20" postplot="" typesetting="extended" ansi="false" ansicolor="[]" elisiondigitsthreshold="10000" showassumed="1" ansilprint="false" trailingsemicolon="true" errorcursor="false" labelling="true" screenheight="25" prompt="M11 &gt; " verboseproc="1" latexwidth="8.0" ShowLabels="true"/>
<Styles>
<Font name="Heading 1" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Warning" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 4" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Line Printed Output" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 2" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="16" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Inert Output" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[144,144,144]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 3" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="14" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Diagnostic" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[40,120,40]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 1" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input" background="[255,255,255]" bold="true" executable="true" family="Courier New" foreground="[120,0,14]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text Output" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 2" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 3" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 4" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 5" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Header and Footer" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="HyperlinkError" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[255,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Atomic Variable" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[175,0,175]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="HyperlinkWarning" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Dictionary Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[147,0,15]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="2D Math" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Bullet Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Plot" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="List Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Dash Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Input" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Error" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[255,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Normal" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Caption Reference" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Code" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input Placeholder" background="[255,255,255]" bold="true" executable="true" family="Courier New" foreground="[200,0,200]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="true"/>
<Font name="Equation Label" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Author" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,128,128]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Caption Text" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Layout name="Heading 1" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="4" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Warning" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 4" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Line Printed Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 2" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="2" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Maple Output" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.3" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 3" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Diagnostic" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 1" alignment="left" bullet="numeric" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix="."/>
<Layout name="Text Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="newline" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 2" alignment="left" bullet="alphabetic" firstindent="0" leftmargin="36" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix="."/>
<Layout name="Ordered List 3" alignment="left" bullet="roman" firstindent="0" leftmargin="72" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix="."/>
<Layout name="Ordered List 4" alignment="left" bullet="ALPHABETIC" firstindent="0" leftmargin="108" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix="."/>
<Layout name="Ordered List 5" alignment="left" bullet="ROMAN" firstindent="0" leftmargin="144" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix="."/>
<Layout name="Annotation Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="HyperlinkError" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="HyperlinkWarning" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Bullet Item" alignment="left" bullet="dot" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Maple Plot" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="List Item" alignment="left" bullet="indent" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Dash Item" alignment="left" bullet="dash" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Error" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Normal" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Author" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="8" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Pencil-style name="Pencil 1" pen-color="[0,0,0]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 2" pen-color="[0,0,255]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 3" pen-color="[0,0,0]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 4" pen-color="[0,0,255]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 5" pen-color="[255,0,0]" pen-height="5.0" pen-width="5.0" pen-opacity="1.0"/>
<Highlighter-style name="Highlighter 5" pen-color="[255,255,0]" pen-height="48.0" pen-width="48.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 3" pen-color="[51,255,0]" pen-height="24.0" pen-width="24.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 4" pen-color="[0,255,255]" pen-height="32.0" pen-width="32.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 1" pen-color="[255,153,255]" pen-height="12.0" pen-width="8.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 2" pen-color="[255,204,0]" pen-height="14.0" pen-width="14.0" pen-opacity="0.8"/>
</Styles>
<Startup-Code startupcode=""/>
<Task-table>
    <Task-category name="&lt;default&gt;"/>
</Task-table>
<Task/>
<Section collapsed="false" isCollapsible="false" drawButton="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1"></Text-field></Title><Text-field style="Text" layout="Bullet Item">The <Font opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" style="Help Maple Name" placeholder="false" family="Times New Roman" font_style_name="Help Maple Name">ExteriorDerivative</Font> command can also be applied to a list of differential forms.</Text-field><Text-field style="Text" layout="Bullet Item">This command is part of the DifferentialGeometry package, and so can be used in the form ExteriorDerivative(...) only after executing the command with(DifferentialGeometry).  It can always be used in the long form DifferentialGeometry:-ExteriorDerivative.</Text-field>
</Section>
<Section collapsed="false" isCollapsible="false" drawButton="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field bookmark="examples" style="Heading 2" layout="Heading 2">Examples</Text-field></Title>
</Section><Presentation-Block>
<Group view="presentation" hide-output="false" inline-output="false" labelreference="L1" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" inline-output="false" labelreference="L7" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group>
<Group view="presentation" hide-output="false" inline-output="false" labelreference="L9" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSV3aXRoRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2Ji1GLDYlUSxMaWVBbGdlYnJhc0YnRjRGNy8lK2V4ZWN1dGFibGVHRkIvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnRj5GPkZobkY+LUY7Ni1RIjpGJ0Y+RkBGQ0ZFRkdGSUZLRk0vRlBRLDAuMjc3Nzc3OGVtRicvRlNGX29GZm5GaG5GPg==">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</Equation></Text-field>
</Input>
</Group>
<Group view="presentation" hide-output="false" inline-output="false" labelreference="L22" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGNC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJ0YrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGNC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJ0YrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-output="false" inline-output="false" labelreference="L5" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Font bold="true">Example 1.</Font></Text-field><Text-field style="Text" layout="Normal">We initialize a 3-dimensional manifold with coordinates <Font opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" style="Help Maple Name" placeholder="false" family="Times New Roman" font_style_name="Help Maple Name">[x, y, z]</Font>.</Text-field><Text-field style="Text" layout="Normal">We use the <Font opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" style="Help Maple Name" placeholder="false" family="Times New Roman" font_style_name="Help Maple Name">declare</Font> command in <Font opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" style="Help Maple Name" placeholder="false" family="Times New Roman" font_style_name="Help Maple Name"> PDEtools</Font> to display the partial derivatives of the functions <Font opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" style="Help Maple Name" placeholder="false" family="Times New Roman" font_style_name="Help Maple Name">a(x, y, z)</Font>, <Font opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" style="Help Maple Name" placeholder="false" family="Times New Roman" font_style_name="Help Maple Name">b(x, y, z)</Font> and <Font opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" style="Help Maple Name" placeholder="false" family="Times New Roman" font_style_name="Help Maple Name">c(x, y, z)</Font> in compact form.</Text-field><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" inline-output="false" labelreference="L20" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L10" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L11" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L12" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L13" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYmUTNFeHRlcmlvckRlcml2YXRpdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjtRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlQtSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSkmb21lZ2E7MUYnRjRGN0Y6RjdGQUY3RkFGN0ZBRisvJStleGVjdXRhYmxlR0ZFRkE=">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" inline-output="false" labelreference="L14" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The exterior derivative of a 2-form:</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L18" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L19" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" inline-output="false" labelreference="L26" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Font bold="true">Example 2.</Font></Text-field><Text-field style="Text" layout="Normal">By way of an example, we illustrate the fact that <Font opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" style="Help Maple Name" placeholder="false" family="Times New Roman" font_style_name="Help Maple Name">d^2 = 0</Font>.</Text-field>
</Input>
</Group>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L23" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2KS1GLDYmUSkmb21lZ2E7M0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSkmQXNzaWduO0YnRjcvRjtRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQtRiw2JlEnZXZhbERHRidGNEY3RjotRj42LVEwJkFwcGx5RnVuY3Rpb247RidGQUZDRkZGSEZKRkxGTkZQL0ZTUSYwLjBlbUYnL0ZWRmhuLUkobWZlbmNlZEdGJDYlLUYjNilGKy1GIzYoRistRiM2KUYrLUYjNictRiw2JlEkZXhwRicvRjVGRUY3RkFGWi1GW282JS1GIzYlLUYsNiZRInlGJ0Y0RjdGOkY3RkFGN0ZBRjdGQS1GPjYtUTEmSW52aXNpYmxlVGltZXM7RidGQUZDRkZGSEZKRkxGTkZQRmduRmluLUYjNictRiw2JlEkY29zRidGaG9GN0ZBRlotRltvNiUtRiM2JS1GLDYmUSJ6RidGNEY3RjpGN0ZBRjdGQUY3RkFGK0Y3RkFGYHAtRiw2JlEjZHhGJ0Y0RjdGOkY3RkEtRj42LlEnJnBsdXM7RidGN0ZBRkNGRkZIRkpGTEZORlAvRlNRLDAuMjIyMjIyMmVtRicvRlZGZnEtRiM2KEYrLUYjNilGKy1GIzYnLUYsNiZRI2xuRidGaG9GN0ZBRlotRltvNiUtRiM2JS1GLDYmUSJ4RidGNEY3RjpGN0ZBRjdGQUY3RkFGYHAtRiM2Jy1GLDYmUSRzaW5GJ0Zob0Y3RkFGWkZpb0Y3RkFGK0Y3RkFGYHAtRiw2JlEjZHpGJ0Y0RjdGOkY3RkFGK0Y3RkFGN0ZBRjdGQUYrLyUrZXhlY3V0YWJsZUdGRUZB">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L27" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L28" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" inline-output="false" labelreference="L31" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Font bold="true">Example 3.</Font></Text-field><Text-field style="Text" layout="Normal">The <Font opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" style="Help Maple Name" placeholder="false" family="Times New Roman" font_style_name="Help Maple Name">ExteriorDerivative</Font> command can also be applied to a list of forms or a matrix of forms.</Text-field>
</Input>
</Group>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L29" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L32" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L33" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" inline-output="false" labelreference="L36" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Font bold="true">Example 4.</Font></Text-field><Text-field style="Text" layout="Normal">The <Font opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" style="Help Maple Name" placeholder="false" family="Times New Roman" font_style_name="Help Maple Name">ExteriorDerivative</Font> command can also be used with adapted frames.  First we define an adapted coframe for <Font opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" style="Help Maple Name" placeholder="false" family="Times New Roman" font_style_name="Help Maple Name">M</Font>.</Text-field>
</Input>
</Group>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L34" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2KS1GLDYmUSNGckYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSkmQXNzaWduO0YnRjcvRjtRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQtRiw2JlEnZXZhbERHRidGNEY3RjotRj42LVEwJkFwcGx5RnVuY3Rpb247RidGQUZDRkZGSEZKRkxGTkZQL0ZTUSYwLjBlbUYnL0ZWRmhuLUkobWZlbmNlZEdGJDYlLUZbbzYnLUYjNitGKy1GIzYpRistRiM2KUYrLUYjNictRiw2JlEieEYnRjRGN0Y6LUY+Ni1RMSZJbnZpc2libGVUaW1lcztGJ0ZBRkNGRkZIRkpGTEZORlBGZ25GaW4tRiw2JlEjZHhGJ0Y0RjdGOkY3RkEtRj42LlEnJnBsdXM7RidGN0ZBRkNGRkZIRkpGTEZORlAvRlNRLDAuMjIyMjIyMmVtRicvRlZGZHAtRiM2Jy1GLDYmUSJ5RidGNEY3RjpGam8tRiw2JlEjZHlGJ0Y0RjdGOkY3RkFGK0Y3RkFGYHAtRiM2Jy1GLDYmUSJ6RidGNEY3RjpGam8tRiw2JlEjZHpGJ0Y0RjdGOkY3RkFGK0Y3RkEtRj42LlEiLEYnRjdGQUZDL0ZHRjZGSEZKRkxGTkZQRmduL0ZWUSwwLjMzMzMzMzNlbUYnLUYjNilGKy1GIzYnRmdvRmpvRltxRjdGQUZgcC1GIzYnRmhwRmpvRmNxRjdGQUYrRjdGQUZmcS1GIzYnRmdvRmpvRmNxRjdGQUYrRjdGQUY3RkEvJSVvcGVuR1EnJmxzcWI7RicvJSZjbG9zZUdRJyZyc3FiO0YnRjdGQUY3RkFGKy8lK2V4ZWN1dGFibGVHRkVGQQ==">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L37" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2KS1GLDYmUSdGckRhdGFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEpJkFzc2lnbjtGJ0Y3L0Y7USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZULUYsNiZRKkZyYW1lRGF0YUYnRjRGN0Y6LUY+Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRkFGQ0ZGRkhGSkZMRk5GUC9GU1EmMC4wZW1GJy9GVkZobi1JKG1mZW5jZWRHRiQ2JS1GIzYnLUYsNiZRI0ZyRidGNEY3RjotRj42LlEiLEYnRjdGQUZDL0ZHRjZGSEZKRkxGTkZQRmduL0ZWUSwwLjMzMzMzMzNlbUYnLUYsNiZRIlBGJ0Y0RjdGOkY3RkFGN0ZBRjdGQUYrLyUrZXhlY3V0YWJsZUdGRUZB">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L38" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L39" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L40" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" inline-output="false" labelreference="L43" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Font bold="true">Example 5.</Font></Text-field><Text-field style="Text" layout="Normal">The <Font opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" style="Help Maple Name" placeholder="false" family="Times New Roman" font_style_name="Help Maple Name">ExteriorDerivative</Font> command can be used with Lie algebras.</Text-field>
</Input>
</Group>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L41" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L44" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L45" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYmUTNFeHRlcmlvckRlcml2YXRpdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjtRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlQtSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSkmdGhldGE7MUYnRjRGN0Y6RjdGQUY3RkFGN0ZBRisvJStleGVjdXRhYmxlR0ZFRkE=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" inline-output="false" labelreference="L48" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Font bold="true">Example 6.</Font> </Text-field><Text-field style="Text" layout="Normal">The <Font opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" style="Help Maple Name" placeholder="false" family="Times New Roman" font_style_name="Help Maple Name">ExteriorDerivative</Font> command can also be used with abstract differential forms.    </Text-field>
</Input>
</Group>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L46" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L49" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYmUTNFeHRlcmlvckRlcml2YXRpdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjtRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlQtSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSgmYWxwaGE7RicvRjVGRUY3RkFGN0ZBRjdGQUY3RkFGKy8lK2V4ZWN1dGFibGVHRkVGQQ==">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="false" inline-output="false" labelreference="L50" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYmUTNFeHRlcmlvckRlcml2YXRpdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjtRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlQtSShtZmVuY2VkR0YkNiUtRiM2Ki1GWDYlLUYjNiktRiw2JlEoJmFscGhhO0YnL0Y1RkVGN0ZBLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjNlbUYnLyUmZGVwdGhHRmNvLyUqbGluZWJyZWFrR1ElYXV0b0YnLUY+Ni5RJyZhbXA7d0YnRjdGQUZDRkZGSEZKRkxGTkZQRlJGVUZeby1GLDYmUScmYmV0YTtGJ0Zdb0Y3RkFGN0ZBRjdGQUYrRl5vRlxwRl5vRl9wRjdGQUY3RkFGN0ZBRisvJStleGVjdXRhYmxlR0ZFRkE=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" inline-output="false" labelreference="L51" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Worksheet>